Definition df-at 10546

Description: Define the set of atoms in a Hilbert lattice. An atom is a non-zero element of a lattice such that anything less than it is zero, i.e. it is a smallest non-zero element of the lattice. Definition of atom in [Kalmbach] p. 15. See ela 10547 and elat2 10548 for membership relations.

Assertion

Ref	Expression
df-at	|- Atoms = {x e. CH | 0H <o x}

Detailed syntax breakdown of Definition df-at

Step	Hyp	Ref	Expression
1		cat 9108	. 2 class Atoms
2		c0h 9079	. . . 4 class 0H
3		vx	. . . . 5 set x
4	3	cv 991	. . . 4 class x
5		ccv 9109	. . . 4 class <o
6	2, 4, 5	wbr 2692	. . 3 wff 0H <o x
7		cch 9073	. . 3 class CH
8	6, 3, 7	crab 1694	. 2 class {x e. CH | 0H <o x}
9	1, 8	wceq 992	1 wff Atoms = {x e. CH | 0H <o x}

This definition is referenced by:  ela 10547  atssch 10551

Copyright terms: Public domain